EGR 280 – Mechanics Problem Set 1

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EGR 280 – Mechanics Problem Set 18
Graphics and problem statements © 2004 R.C. Hibbeler.
Published by Pearson Education, Inc., Upper Saddle River, NJ.
18.1 The man pulls the rope off the reel with a
constant force of 8 lb in the direction shown. If
the reel has a weight of 250 lb and a radius of
gyration kA = 0.8 ft, determine the angular velocity
of the reel in 3 s starting from rest. Neglect
friction and the weight of rope removed.
Ans: ω = 6.04 rad/s
18.2 The drum has a mass of 70 kg, a radius of
300 mm and radius of gyration kO = 125 mm. If
μs= 0.4 and μk = 0.3, determine the drum’s angular
velocity 2 s after it is released from rest. Take θ =
30°.
Ans: ω = 27.9 rad/s
18.3 The crate has a mass mc. Determine the
constant speed vo it acquires as it moves down the
conveyor. Treat the rollers as thin rings with have
mass m, radius r and spaced d apart. Note that
friction causes each roller to rotate when the crate
comes in contact with it.
Ans: v02 = (2gdmc/m) sinθ
18.4 The man sits on the swivel chair holding two
5-lb weights with his arms outstretched. If he is
turning at 3 rad/s in this position, determine his
angular velocity when the weights are drawn in
and held 0.3 ft from the axis of rotation. Assume
he weighs 160 lb and has a radius of gyration of
kz=0.55 ft about the z-axis. Neglect the mass of
his arms and the size of the weights.
Ans: ω = 6.75 rad/s
18.5 A thin ring having a mass of 15 kg strikes the
20-mm high step. Determine the minimum
angular velocity ω1 the ring can have so that it will
just roll over the step at A when it strikes it.
Ans: ω1 = 2.606 rad/s
18.6 The 6-lb slender rod AB is originally at rest,
suspended in the vertical position. A 1-lb ball is
thrown at the rod with a velocity v = 50 ft/s and
strikes the rod at C. Determine the angular
velocity of the rod just after the impact. Let e =
0.7 and d = 2 ft.
Ans: ω2 = 5.23 rad/s
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